Measuring and Improving Cooling System Performance – Part 6: Physical Model

One of the unfortunate realities of cooling system modification and testing is that we can't visually observe what goes on under the hood while the car is driving. Building a physical model of the cooling system may shed some light on what the real system is doing and can be designed for easy observation if you make a window one side of the duct.

The air filter here functions the same as a heat exchanger in that it restricts flow and dissipates energy in the form of total pressure loss.

Similar to the real cooling system as I decided to analyze it in the previous post, this model has no nozzle outlet. Instead, we have the same as we get in an engine bay: a pressure boundary, meaning an enforced static pressure behind the heat exchanger. Here, that is simply ambient pressure (C_P = 0). While it is not possible to vary atmospheric pressure here, we saw in Part 5 (and will revisit later on) that modifications such as vents can change engine bay static pressure and thus the boundary or outlet conditions on the real exchanger.
 
What we can change here are the inlet conditions. Here's what the flow looks like with the duct as is, an inlet area about half the size of the filter with a smooth-sided duct (I did the curve by eye, so these results were pleasantly surprising):

In this condition, the static pressure difference measured in the center of the filter is about 240 Pa at 75 kph and the tufts show good flow across the whole filter. Blocking half the inlet with a board, either top or bottom, reduces that static pressure difference to 0 Pa. However, as you can see below, in this condition there is still flow through the filter (even accounting for the lower tuft closest to the window, where there is some leakage around the filter):

The tufts reveal something important: conditions are not uniform across the filter (you can see above how they change when the inlet is blocked on either the top or bottom), and they aren’t uniform across the real heat exchanger under the hood either. Even if you measure 0 static pressure drop across the heat exchanger at some location, it doesn’t mean there is no flow through it (as I wrote before, incorrectly!). Further, as we saw in Part 4, the dynamic pressure on both sides of the exchanger will tell us the flow velocity into and out of it, and the total pressure loss across the exchanger reflects its drag, cooling capacity, and the direction of flow. Static pressure measurement alone will not give you enough information about the flow through the exchanger to determine cooling system performance on your car. We'll revisit this idea in just a minute.
 
Core Area and Flow Through Ducts
 
(Before reading this next section, brush up on your definitions of pressure by going through this explainer. The differences between static pressure, dynamic pressure, and total pressure figure heavily in the following discussion).

Recall this chart from Part 4, of dynamic pressure out of the heat exchanger package on my car compared to dynamic pressure in:

…and this chart from Part 3, of velocity into the core as a fraction of freestream:

These actually show us the same thing we can observe in the tufts taped to the model. Measured q₂ and q₃, with a large difference that cannot be explained by density change alone, show that u₃ << u₂. What this means is, due to conservation of mass, A₂ (streamtube area into the core) is actually much smaller than A₃ (streamtube area out of the core), a conclusion that is corroborated by measured core velocity ratio. Inlet area to core area on my car is approximately 0.37, which means the velocity ratio at the heat exchanger should be about the same fraction. But it isn’t; it’s much higher at 0.50. This means the car is not using the whole heat exchanger core area! I may be able to change this by fabricating a smooth inlet diffuser and modifying outlet area and static pressure in the engine bay. As we saw at the end of Part 4, increasing core area and decreasing velocity will reduce drag from the heat exchangers.
 
This brings up an important point regarding the difference between our air filter model and the real heat exchanger: namely, this model doesn't exchange any heat. We aren't adding energy to the flow, so all the energy that comes into the filter as static enthalpy and kinetic energy must come out as static enthalpy, kinetic energy, and dissipation (increased entropy and work done on the filter through shear and the no-slip condition, which is also responsible for the drag force on it). The implication of this is, the velocity of the air coming out of the filter must be less than the velocity going in; however, continuity stipulates that these velocities should be equal in this case (constant area and density, since we aren't changing the temperature of the air). This leads to the conclusion that the flow properties across the filter cannot be uniform, as this would violate the conservation equations. Hence, just because we measure zero static pressure difference in one location on the filter does not mean it is zero everywhere—it just happens to be in that spot (or is too small to measure).
 
In the real heat exchanger, the density of the air going out must be lower than that coming in due to the fact that its temperature has increased. Since the mass flow rate through the core must be constant at steady-state, real heat exchangers have non-uniform flow properties across their cores and so can have a different effective outlet area than inlet to satisfy continuity. We saw this simulated in the first plot in Part 4:

Further, because u₃ is not the same as u₂ and q₃ is not equal to q₂, the static pressure change is not equal to total pressure loss across the heat exchanger (as we saw in Part 4, and you can measure on your own car). What you should take from this, in conjunction with the energy model in Part 4, is that if you want to see how a particular modification affects your car's cooling, you should measure the difference in total pressure (p₀₂ – p₀₃) not just static pressure (p₂ – p₃). This corroborates what we saw in our measurements across the heat exchanger core, where static pressure loss on my car was only about half of total pressure loss.
 
And, as always, don't just take my word for it—go read Hoerner: "The rate of flow through the duct is a function of the difference in total pressure between intake and outlet, and therefore a function of the internal losses of momentum" [9-2, emphasis added]. This is true of any duct—e.g. engine air intake, as Barnard specifically points out—not just the cooling system.
 
The more momentum is lost in the duct, the less mass flow there will be through it. Draw out and consider a duct with some arbitrary internal total pressure loss and you will see that it is perfectly possible to have flow through the duct even with higher outlet static pressure than inlet if the duct is submerged in a flow field (that is, if there is some velocity in the freestream to drive flow into the duct). The static pressure change tells us the direction of the pressure gradient and whether it is adverse (low to high) or favorable (high to low) but it only tells us the direction of flow if u_∞ is zero—that is, if the car is stationary (and in this condition, we use something like a fan behind the heat exchanger to create that static pressure drop, or engine vacuum in the cylinders, or a fan in the HVAC ducting). When the car is moving, the flow is driven by the relative motion between the vehicle and air mass, not just by static pressure changes (which, in a stationary air mass, are equivalent to changes in total pressure). In fact, we can raise or lower static pressure at any point in the duct simply by the choice of cross section area: larger area gives higher static pressure and vice versa (the point you should have taken from our discussion of diffusers and measurement on your own car).
 
I used to think, based on reading lots of online resources that I now realize were quite incorrect, that measuring static pressure loss through a duct such as an engine air intake or air curtain duct would tell me how well it flows, and that airflow could only be "pushed" through a radiator on a moving car by static pressure drop. Neither of these is true. Reality is much more complicated, but the upshot is that the measures of how well a duct flows (i.e. how much energy loss there is in the flow through the duct) and the direction of flow through a duct or across a heat exchanger are both given by changes in total pressure.

The second-generation Viper and Viper ACR used different throttle body tubes: ridged, accordion-style in the base car (top) and smooth in the ACR (bottom). The smooth tubes reduced total pressure loss enough, even in just that short distance, for Chrysler to certify a 10 hp increase in power output, from 450 hp to 460 hp, with no other changes to the engine.

This custom airbox I added to my Viper when I owned it—long before I got into engineering at all—was, in retrospect, a very poor decision. The abrupt area change from the NACA inlet (the opening in the hood, at the top of the image) to airbox, compared to the smooth and gradual stock diffuser, almost certainly increased total pressure loss!

If you still don't believe me, consider a popular thought experiment you may have encountered before. Say you have a car with a cooling air opening, heat exchanger, and a completely sealed engine bay. Start driving the car, and the engine bay soon fills up with air that cannot escape. Once the bay is filled, there will be no more flow through the exchanger. Online, you've seen this explained as the static pressure in the engine bay being high—which it is. But in this hypothetical case, static pressure is equal to total pressure in the engine bay. This is exactly the same thing that happens in a total pressure port:

The flow in the tube is stagnated (decelerated to 0 velocity) because it has no escape route, and the sensor at the other end records total pressure. Similarly, the zero-flow condition through our engine bay and heat exchanger occurs when total pressure behind the exchanger equals total pressure in front of it. If there is flow through the heat exchanger in either direction, there must be total pressure loss across it (otherwise it would violate the 2^nd Law of Thermodynamics)—and, approximating energy added from the coolant as negligible, the direction of total pressure loss tells us the direction of flow. The same is true of engine air intakes, brake cooling ducts, cabin ventilation intakes, air curtain ducts, etc. We'll see a mathematical proof of this in the next post.
 
Grill Blocks
 
Look again at the video of the duct with a block in place. Closing down the inlet area like this should, by conservation of mass, increase static pressure on the front side of the filter. But clearly, it does not—in fact, the opposite occurs. Why? Because we've massively increased the total pressure loss in the duct.
 
With no block in place, the static pressure increase on the front of the filter is almost as much as freestream dynamic pressure q_∞ (based on speed and temperature at the time of testing)—which means the duct is functioning very efficiently, with little total pressure loss and low u_core. Closing down the inlet by blocking half of it also enforces a huge area of separated flow behind the block, and that separation increases energy dissipation and therefore total pressure loss. u_core may very well be lower in this condition (I don't know since I didn't measure total pressure at the filter), but with less available energy in the flow even a small dynamic pressure doesn't leave as much static pressure available as without the block. Looking back at past results of testing grill blocks and measuring static pressure difference across the heat exchangers, this is evident there as well although I did not know enough to interpret those results correctly at the time.

This gives us insight into grill blocking, a popular practice in the ecomodding community. Blocking portions of the grill may reduce drag (by restricting mass flow) but it is not the most efficient way to do that since it increases momentum loss internally and reduces cooling capacity. We'll revisit this in the next two posts, but if we approximate static pressure differences well upstream and downstream of the cooling system as negligible then the internal drag is given by the product of mass flow rate and velocity loss (revisit Part 4 to see how this is derived):

By restricting mass flow at the inlet, grill blocks reduce the first variable ṁ but can increase the second term u_in – u_out (since u_in is constant, based on the car’s speed). It is better to leave the inlet opening as is and reduce mass flow rate by changing the outlet size, since this will reduce the streamtube area captured by the inlet, raising static pressure at the opening, and maintaining more cooling capacity compared to a simple grill block. Additionally, blocking the grill with sharp-edged boards or plastic may increase total pressure losses even more, reducing cooling system efficiency.

OEMs use movable vanes in the inlet to block flow (rather than the outlet, which is typically a very complicated "duct" with lots of restrictions and losses) for one simple reason: it's cheaper, not because it's more effective. You can copy them if you want, but you can also do a lot better. If you want to close down the inlet opening, do so based on outlet area. And do it with both a grill block and a smooth-sided diffuser duct to minimize total pressure loss. That way, higher static pressure p₂ (low u_core) and high diffuser efficiency can be preserved. If you want to vary cooling airflow—the point of those shutters—do it by closing or opening outlet area.
 
(Note that some manufacturers also use vanes to direct flow upward or downward in the diffuser duct, such as Rivian on their R1 series. If you want to experiment with this on your car, these don't need to move or block off the opening if your outlet is sized and conditioned properly).
 
Model Revision
 
Since the results of the first model were so interesting, I decided to revise the duct to better reflect the dimensions of the cooling system in my car. Using the same ratio of inlet height and diffuser length to core height as on the real car, this looks like:

…with the upper curve here approximating the shape of the bumper cover and a much shorter duct overall. Here's what the flow looks like now:

And with a smooth diffuser duct fitted inside, again approximating the dimensions of what I could fit on the actual car (which means it has to fit underneath and around the crash structure):

The flow here in "stock" configuration is not as bad as I expected, although there is still noticeable non-uniformity. Adding the interior duct improves this; the tufts here look almost the same as with the longer, open duct above. I should be able to shape the real duct better than this, with more curvature at the top of the heat exchanger and a gentler curve around the bumper beam, so I expect it to perform even better than this approximation, with an appropriately sized inlet and perhaps modification of the outlet opening behind the fans.
 
How big should our inlet and outlet be, and how should we go about modifying the system for lower drag and improved cooling? We’ll figure that out next time, when we step through the entire system from inlet to outlet in order to determine how to make it better.

Previous: Measuring and Improving Cooling System Performance – Part 5: Fan and Outlet